I converted a Roth IRA in 1998 and spread the payments over 4 years. Now the value of the IRA has dropped about 50% (admittedly due to some poor investing on my part).

While I understand that this was a risk when converting, do I have any options to reduce my tax liability this year? Essentially I am paying taxes on a quarter of the original amount, which has been lost.

Any advice? Can I somehow recharacterize the IRA and bring down to my current value? Or, can I claim losses on the IRA to reduce my income?

You cannot recharacterize the conversion if the conversion was proper when made. As for closing the account and deducting losses, see my article on this subject on my web site, www.bpickercpa.com. My guess is that it won't pay to do so.